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On convex bodies in , , with directly congruent projections 在凸体上，有直接全等的投影
IF 0.8 3区 数学
Mathematika Pub Date : 2025-02-06 DOI: 10.1112/mtk.70011
Reema A. Sbeih
{"title":"On convex bodies in , , with directly congruent projections","authors":"Reema A. Sbeih","doi":"10.1112/mtk.70011","DOIUrl":"https://doi.org/10.1112/mtk.70011","url":null,"abstract":"<p>Let <span></span><math></math> and let <span></span><math></math> and <span></span><math></math> be two convex bodies in <span></span><math></math> such that their orthogonal projections <span></span><math></math> and <span></span><math></math> onto any <span></span><math></math>-dimensional subspace <span></span><math></math> are directly congruent, that is, there exists a rotation <span></span><math></math> and a vector <span></span><math></math> such that <span></span><math></math>. Assume also that the 2-dimensional projections of <span></span><math></math> and <span></span><math></math> are pairwise different and they do not have <span></span><math></math>-symmetries. Then <span></span><math></math> and <span></span><math></math> are congruent. We also prove an analogous more general result about twice differentiable functions on the unit sphere in <span></span><math></math>.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lattices in function fields and applications 函数域中的格及其应用
IF 0.8 3区 数学
Mathematika Pub Date : 2025-01-31 DOI: 10.1112/mtk.70010
Christian Bagshaw, Bryce Kerr
{"title":"Lattices in function fields and applications","authors":"Christian Bagshaw,&nbsp;Bryce Kerr","doi":"10.1112/mtk.70010","DOIUrl":"https://doi.org/10.1112/mtk.70010","url":null,"abstract":"<p>In recent decades, the use of ideas from Minkowski's Geometry of Numbers has gained recognition as a helpful tool in bounding the number of solutions to modular congruences with variables from short intervals. In 1941, Mahler introduced an analogue to the Geometry of Numbers in function fields over finite fields. Here, we build on Mahler's ideas and develop results useful for bounding the sizes of intersections of lattices and convex bodies in <span></span><math></math>, which are more precise than what is known over <span></span><math></math>. These results are then applied to various problems regarding bounding the number of solutions to congruences in <span></span><math></math>, such as the number of points on polynomial curves in low-dimensional subspaces of finite fields. Our results improve on a number of previous bounds due to Bagshaw, Cilleruelo, Shparlinski and Zumalacárregui. We also present previous techniques developed by various authors for estimating certain energy/point counts in a unified manner.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143121401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On differences of two harmonic numbers 关于两个调和数的差
IF 0.8 3区 数学
Mathematika Pub Date : 2025-01-27 DOI: 10.1112/mtk.70009
Jeck Lim, Stefan Steinerberger
{"title":"On differences of two harmonic numbers","authors":"Jeck Lim,&nbsp;Stefan Steinerberger","doi":"10.1112/mtk.70009","DOIUrl":"https://doi.org/10.1112/mtk.70009","url":null,"abstract":"<p>We prove the existence of infinitely many <span></span><math></math> such that the difference of harmonic numbers <span></span><math></math> approximates 1 well\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coherency properties for monoids of transformations and partitions 变换和划分的模群的相干性
IF 0.8 3区 数学
Mathematika Pub Date : 2025-01-08 DOI: 10.1112/mtk.70005
Matthew Brookes, Victoria Gould, Nik Ruškuc
{"title":"Coherency properties for monoids of transformations and partitions","authors":"Matthew Brookes,&nbsp;Victoria Gould,&nbsp;Nik Ruškuc","doi":"10.1112/mtk.70005","DOIUrl":"https://doi.org/10.1112/mtk.70005","url":null,"abstract":"<p>A monoid <span></span><math></math> is <i>right coherent</i> if every finitely generated subact of every finitely presented right <span></span><math></math>-act itself has a finite presentation; it is <i>weakly right coherent</i> if every finitely generated right ideal of <span></span><math></math> has a finite presentation. We show that full and partial transformation monoids, symmetric inverse monoids and partition monoids over an infinite set are all weakly right coherent, but that none of them is right coherent. Left coherency and weak left coherency are defined dually, and the corresponding results hold for these properties. In order to prove the non-coherency results, we give a presentation of an inverse semigroup which does not embed into any left or right coherent monoid.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complements of unions: Insights on spaceability and applications 联合的补充：关于空间性和应用的见解
IF 0.8 3区 数学
Mathematika Pub Date : 2025-01-08 DOI: 10.1112/mtk.70006
Gustavo Araújo, Anderson Barbosa, Anselmo Baganha Raposo Jr., Geivison Ribeiro
{"title":"Complements of unions: Insights on spaceability and applications","authors":"Gustavo Araújo,&nbsp;Anderson Barbosa,&nbsp;Anselmo Baganha Raposo Jr.,&nbsp;Geivison Ribeiro","doi":"10.1112/mtk.70006","DOIUrl":"https://doi.org/10.1112/mtk.70006","url":null,"abstract":"<p>This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the results of Kitson and Timoney [J. Math. Anal. Appl. <b>378</b> (2011), 680–686]. This criterion extends and recovers some classical results in this theory. The second criterion establishes sufficient conditions for the complement of a union of Lebesgue spaces to be <span></span><math></math>-spaceable, or not, even when they are not locally convex. We use this result to characterize measurable subsets having positive measure. Armed with these results, we have improved existing results in environments such as Lebesgue measurable function sets, spaces of continuous functions, sequence spaces, nowhere Hölder function sets, Sobolev spaces, non-absolutely summing operator spaces and even sets of functions of bounded variation.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Diagonal cubic forms and the large sieve 对角立方形式和大筛子
IF 0.8 3区 数学
Mathematika Pub Date : 2025-01-02 DOI: 10.1112/mtk.70008
Victor Y. Wang
{"title":"Diagonal cubic forms and the large sieve","authors":"Victor Y. Wang","doi":"10.1112/mtk.70008","DOIUrl":"https://doi.org/10.1112/mtk.70008","url":null,"abstract":"<p>Let <span></span><math></math> be the number of integral zeros <span></span><math></math> of <span></span><math></math>. Works of Hooley and Heath-Brown imply <span></span><math></math>, if one assumes automorphy and grand Riemann hypothesis for certain Hasse–Weil <span></span><math></math>-functions. Assuming instead a natural large sieve inequality, we recover the same bound on <span></span><math></math>. This is part of a more general statement, for diagonal cubic forms in <span></span><math></math> variables, where we allow approximations to Hasse–Weil <span></span><math></math>-functions.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The radial symmetry of minimizers to the weighted Dirichlet energy in 最小值对加权狄利克雷能量的径向对称性
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-28 DOI: 10.1112/mtk.70007
David Kalaj
{"title":"The radial symmetry of minimizers to the weighted Dirichlet energy in","authors":"David Kalaj","doi":"10.1112/mtk.70007","DOIUrl":"https://doi.org/10.1112/mtk.70007","url":null,"abstract":"<p>Let <span></span><math></math> and <span></span><math></math> be annuli in <span></span><math></math>. Let <span></span><math></math>, and assume that <span></span><math></math> is the class of Sobolev <span></span><math></math> homeomorphisms of <span></span><math></math> onto <span></span><math></math>. Then, we consider the following Dirichlet-type energy of <span></span><math></math>:\u0000\u0000 </p><p>For general <span></span><math></math>, we minimize the Dirichlet-type integral <span></span><math></math> throughout the class of radial mappings between given annuli, and this minimum always exists for <span></span><math></math>. For <span></span><math></math>, the image annulus cannot be too thick, which is opposite to the Nitsche-type phenomenon known for the standard Dirichlet energy, where the image annulus cannot be too thin.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the zeros of odd weight Eisenstein series 在奇权爱森斯坦级数的零点上
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-22 DOI: 10.1112/mtk.70004
Jan-Willem van Ittersum, Berend Ringeling
{"title":"On the zeros of odd weight Eisenstein series","authors":"Jan-Willem van Ittersum,&nbsp;Berend Ringeling","doi":"10.1112/mtk.70004","DOIUrl":"https://doi.org/10.1112/mtk.70004","url":null,"abstract":"<p>We count the number of zeros of the holomorphic odd weight Eisenstein series in all <span></span><math></math>-translates of the standard fundamental domain.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lower bounds for the large deviations of Selberg's central limit theorem 塞尔伯格中心极限定理大偏差的下界
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-11 DOI: 10.1112/mtk.70002
Louis-Pierre Arguin, Emma Bailey
{"title":"Lower bounds for the large deviations of Selberg's central limit theorem","authors":"Louis-Pierre Arguin,&nbsp;Emma Bailey","doi":"10.1112/mtk.70002","DOIUrl":"https://doi.org/10.1112/mtk.70002","url":null,"abstract":"<p>Let <span></span><math></math> and <span></span><math></math>. We prove that, for any <span></span><math></math> and <span></span><math></math> as <span></span><math></math>,\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the family of singular Brascamp–Lieb inequalities with dimension datum (1,2,2,1) 关于维数为（1,2,2,1）的奇异Brascamp-Lieb不等式族
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-08 DOI: 10.1112/mtk.70003
Fred Yu-Hsiang Lin
{"title":"On the family of singular Brascamp–Lieb inequalities with dimension datum (1,2,2,1)","authors":"Fred Yu-Hsiang Lin","doi":"10.1112/mtk.70003","DOIUrl":"https://doi.org/10.1112/mtk.70003","url":null,"abstract":"<p>Motivated by the triangular Hilbert transform, we classify a certain family of singular Brascamp–Lieb forms which we associate with the dimension datum (1,2,2,1). We determine the exact range of Lebesgue exponents, for which one has singular Brascamp–Lieb inequalities within this family. The remaining observations concern counter examples to boundedness. We compare with a counter-example showing that the triangular Hilbert form does not satisfy singular Brascamp–Lieb bounds in the endpoints.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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